With respect, @whereskarlo, you have been ignoring answers to your questions. @sharpdrivetek answered your question in post #2. I answered your question in post #4 and repeated the answer in post #6. Both of us gave the reason why.
I am a forum moderator, not the developer. But that does not make the answers you are getting incorrect.
Once again, you have failed to read the answers provided. Let me try to explain things differently. The Search function returns results from the data already presented. Since sales order numbers are not there, it cannot return them. The reasons they are not there are (1) sales orders have no financial impact, so they are not in the data being searched and (2) even if they were, the transactions affecting quantity on hand occur at the line-item level, where no reference numbers exist. Further, there is no way for a user to add columns to search results, especially not for data that does not exist.
As a result, going back to the subject of this thread, you cannot add a column for sales order numbers (or anything else) to inventory search results.